In high school some of you learned about, or were subjected to quadratic equations. They looked something like this, and you were shown a potentially tedious procedure, that, if followed carefully would yield a pair of solutions for the ``unknown quantity'', $x$ in the equation. To me this was fun, but not
particularly wonderful. What I found totally incredible was the fact that a single formula exists which brings together all possible quadratic equations and solves them simultaneously. It even tells you whether or not a
solution exists, and if not, why not. The so-called quadratic formula, highlighted here in grey, was to me beautiful, in its ability to bring together these diverse equations into a single, elegant framework.
Now of course, to some of you, such an equation, in fact this whole slide, looks more or less like a jumble of lines and squiggles, with no aesthetic value.